Mathematics (MMath)

The
four-year MMath programme provides the opportunity to delve more deeply into
pure and applied mathematics than is possible on a BSc course. The programme
is an ideal preparation if you want to go on to research work in mathematics,
work for a technological company or simply want to gain a deeper understanding
of mathematics, and develop skills which are in demand by a range of prospective
employers.

The MMath degree programme is offered to satisfy a need for a more advanced
level of mathematical training than is available in a 3-year programme.
The modules offered in the first three years of the programme are common
to the 3-year degree programmes in mathematics, allowing the flexibility
of transfer between courses.

In the first year you study a variety of mathematics and computing modules.
In the second and third years you take a selection of advanced modules that
allow you to build on the interests developed in the first year.

In the fourth year the course develops research training and enhanced
mathematical skills, especially in Mathematical Analysis, Mathematical Physics
and Fluid Dynamics. There is also a major piece of project work in which
you would be undertaking novel research. The course is an ideal preparation
for students wishing to go on to research work in mathematics, work for
a technological company or who simply want to gain a deeper understanding
of mathematics, and it is highly regarded by prospective employers.

The course structure is given below. All modules are 10 credits unless
otherwise stated.

Year One

You will study the following core modules:

Calculus

Elementary Differential Equations

Algebra I and II

Analysis I and II

Dynamical Systems and Chaos

Introduction to Probability Theory

Computing Skills

Number Theory I

Numerical Analysis I

And 10 credits of optional modules from :

Mechanics I

Statistical Inference

Year Two

Specialisation continues in the second year.

You will study the following core modules:

Calculus of Several Variables

Matrix Algebra

Complex Analysis

Series and Transforms

Analysis III

Linear Algebra

Numerical Analysis II

Vector Calculus

And 40 credits from the following optional modules:

Number Theory II

Modelling with Differential Equations

Mechanics II

Elementary Fluid Dynamics

Ordinary Differential Equations

Operational Research (20 credits)

Foundations of Probability and Statistics (20 credits)

Year Three

You will study the following core modules:

Coding Theory and Data Compression (20 credits)

Functional and Fourier Analysis (20 credits)

Combinatorics

Differential Geometry

And 60 credits from the following optional modules:

Methods of Applied Mathematics (20 credits)

Theoretical and Computational PDE’s (20 credits)

Knots

Groups, Rings and Fields

Complex Function Theory

Applied Nonlinear Systems

Fluid Dynamics

Mathematical Programming

Discrete Optimisation

Mathematical Statistics

Time Series Analysis and Forecasting

Year Four

You will study:

MMath Project (40 credits)

And 80 credits from the following modules:

Operator Algebras and Non-Commutative Geometry (20 credits)

Functional Analysis (20 credits)

Computational Fluid Dynamics (20 credits)

Measure Theory (20 credits)

Mathematical Principles of Image Processing (20 credits)

Reading Module (20 credits)

The School of Mathematics has a reputation for excellent teaching quality
standards, a friendly atmosphere that pervades the School, and the care
and support students receive from the staff. The School strives to ensure
that its students react enthusiastically to their courses and thoroughly
enjoy their learning experience.

The School offers a range of research-led teaching and learning opportunities
which develop essential mathematical and employability skills. Teaching
is carried out through a blend of lectures, tutorials and examples classes
(laboratory classes where appropriate), including a major project component
with an element of formal instruction in research methods and presentation
skills in the fourth year. To aid the transition to University, all first
year modules have associated tutorial sessions that promote peer interaction
and discussion. For the majority of first year modules, welsh language tutorials are also available. Increased independent learning is encouraged throughout
the programme and particularly in year four, some lectures will take more
of a seminar style format.

In all years the classes are used to discuss both theoretical concepts
and essential mathematical techniques. Students are encouraged to undertake
additional reading outside of timetabled classes and fully engage with and
reflect upon the formative/summative assessments that take place. Summative
assessment is mainly through written examination that takes place either
at the end of the Autumn or Spring Semester, but many modules involve an
element of continuous assessment which includes problem solving exercises,
written reports, computer programs, oral presentation etc. Feedback on progress
is typically provided through a combination of discussion in class, written
comments on submitted work and review of outline solutions to problems.

The degree award will be based on 20% from your Year 2 studies, 30% from
Year 3, and 50% from Year 4.

All students are allocated a Personal Tutor for the duration of the Programme,
from whom they can expect to receive pastoral advice, guidance and support.
Students are encouraged to utilise personal tutors to reflect upon their
academic and personal development, as well as future employment opportunities.
To aid this process, an extensive online Personal Development Planning module
is available to all students via Learning Central (Cardiff University’s
Virtual Learning Environment).

Although Personal Tutors do not have a formal role in the teaching process
most tutors are very happy to provide academic help when possible and students
are encouraged to approach them at any time. In addition, students are encouraged
to discuss any queries related to specific modules with individual lecturers.
Module information and related resources are also made available to students
via Learning Central.

The Mathematics degree programmes at Cardiff will equip you with specialist
numerical skills and develop your capacity for logical and analytical thought.
These are qualities which are in demand across a broad range of stimulating
and rewarding careers.

In addition to the formal teaching on the programme the School of Mathematics
also has significant engagement with the Careers Service and Employers.
This includes a Careers Management Skills Programme, numerous company presentations
held in the School, presentations by students returning from industry, and
a range of sponsored prizes awarded for academic achievement.

In 2010, 57% of the School’s graduates were in employment within six months
of graduation while a further 28% were engaged in further study with others
taking time out to travel etc.

Employers included: universities, banks plus organisations such as the
Office of National Statistics and the Meteorological Office. Career destinations
included: finance manager, lecturer, risk analyst and statistician.